Answer :
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal.
If we have the following line:
[tex]y = x[/tex]
Whose slope is [tex]m_ {1} = 1[/tex]
So, a line parallel to it has a slope [tex]m_ {2} = 1[/tex]
Therefore, the equation is of the form:
[tex]y = x + b[/tex]
If the line passes through point [tex](2,4),[/tex] we can substitute in the equation and find "b":
[tex]4 = 2 + b\\4-2 = b\\b = 2[/tex]
Finally, the equation is:
[tex]y = x + 2[/tex]
ANswer:
[tex]y = x + 2[/tex]